Finite Group Databasebeta

← #8467082

Subgroups — #8467082

Order 512.

3933 conjugacy classes of subgroups.

The subgroup lattice has 1517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59445C211yesmaximal, characteristic, complemented
2#59435C211yesmaximal, characteristic
3#59429C211yesmaximal, characteristic
4#57690C214yesmaximal, complemented
5#56536C214yesmaximal, complemented
6#55385C214yesmaximal, complemented
7#53107C212yesmaximal, complemented
8#53036C212yesmaximal, complemented
9#50056C214yesmaximal, complemented
10#46347C212yesmaximal
11#46069C212yesmaximal, complemented
12#45403C212yesmaximal
13#45219C212yesmaximal, complemented
14#42972C212yesmaximal, complemented
15#42845C212yesmaximal
16#42774C212yesmaximal, complemented
17#42728C212yesmaximal, complemented
18#40075C212yesmaximal, complemented
19#39754C212yesmaximal, complemented
20#39635C211yesmaximal, characteristic, complemented
21#39180C211yesmaximal, characteristic, complemented
22#39081C212yesmaximal, complemented
23#38977C211yesmaximal, characteristic
24#38966C211yesmaximal, characteristic
25#38227C212yesmaximal, complemented
26#37637C211yesmaximal, characteristic
27#37353C212yesmaximal
28#37328C212yesmaximal, complemented
29#36574C211yesmaximal, characteristic, complemented
30Q8×#125C211yesmaximal, characteristic, complemented
31#36312C211yesmaximal, characteristic
32#35208C211yesmaximal, characteristic, complemented
33#35208C211yesmaximal, characteristic, complemented
34#34951C211yesmaximal, characteristic, complemented
35#34902C211yesmaximal, characteristic
36#2863C2212yes—
37#2863C2212yes—
38#2860C2212yes—
39#2859C2211yescharacteristic
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2859C2212yes—
43#2859C2212yes—
44#2859C2212yes—
45#2845C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2839C2214yes—
49#2836C2214yes—
50#2831C2214yes—
51#2831C2214yes—
52#2822C2214yes—
53#2802C2214yes—
54#2802C2214yes—
55#2802C2214yes—
56#2802C2214yes—
57#2794C2214yes—
58#2794C2214yes—
59#2793C2214yes—
60#2791C2214yes—
61#2790C2214yes—
62#2790C2214yes—
63#2788C2214yes—
64#2783C2214yes—
65#2783C2214yes—
66#2777C2214yes—
67#2776C2214yes—
68#2775C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2774C2214yes—
72#2772C2214yes—
73#2771C2214yes—
74#2769C2214yes—
75#2768C2214yes—
76#2768C2214yes—
77#2767C2214yes—
78#2767C2214yes—
79#2766C2214yes—
80#2766C2214yes—
81#2765C2214yes—
82#2758C2214yes—
83#2755C2214yes—
84#2744C2214yes—
85#2739C2214yes—
86#2738C2214yes—
87#2738C2214yes—
88#2729C2214yes—
89#2726C2214yes—
90#2725C2214yes—
91#2725C2214yes—
92#2725C2214yes—
93#2725C2214yes—
94#2722C2214yes—
95#2722C2214yes—
96#2721C2214yes—
97#2721C2214yes—
98#2719C2214yes—
99#2719C2214yes—
100#2704C2214yes—
101#2689C2214yes—
102#2666C2214yes—
103#2666C2214yes—
104#2660C2214yes—
105#2655C2214yes—
106#2654C2214yes—
107#2652C2214yes—
108#2647C2212yes—
109#2647C2212yes—
110#2647C2214yes—
111#2647C2212yes—
112#2645C2212yes—
113#2644C2212yes—
114#2637C2214yes—
115#2629C2212yes—
116#2629C2212yes—
117#2625C2212yes—
118#2612C2214yes—
119#2604C2214yes—
120#2596C2212yes—
121#2596C2214yes—
122#2594C2212yes—
123#2592C2211yescharacteristic
124#2585C2212yes—
125#2585C2212yes—
126#2584C2212yes—
127#2584C2212yes—
128#2584C2212yes—
129#2582C2212yes—
130#2582C2211yescharacteristic
131#2582C2211yescharacteristic
132#2582C2211yescharacteristic
133#2581C2212yes—
134#2581C2211yescharacteristic
135#2581C2212yes—
136#2575C2214yes—
137#2571C2212yes—
138#2571C2214yes—
139#2570C2212yes—
140#2570C2211yescharacteristic
141#2570C2212yes—
142#2570C2214yes—
143#2568C2211yescharacteristic
144#2567C2211yescharacteristic
145#2567C2211yescharacteristic
146#2567C2211yescharacteristic
147#2566C2212yes—
148#2563C2211yescharacteristic
149#2552C2211yescharacteristic
150#2552C2211yescharacteristic
151#2552C2212yes—
152#2552C2212yes—
153#2552C2212yes—
154#2552C2211yescharacteristic
155#2552C2212yes—
156#2552C2211yescharacteristic
157#2552C2212yes—
158#2550C2212yes—
159#2546C2211yescharacteristic
160#2545C2211yescharacteristic
161#2538C2211yescharacteristic
162#2538C2212yes—
163#2533C2214yes—
164#2529C2214yes—
165#2528C2214yes—
166#2528C2214yes—
167#2525C2212yes—
168#2524C2214yes—
169#2519C2214yes—
170#2519C2214yes—
171#2515C2214yes—
172#2514C2211yescharacteristic
173#2512C2212yes—
174#2512C2212yes—
175#2512C2211yescharacteristic
176#2511C2212yes—
177#2511C2212yes—
178#2511C2212yes—
179#2511C2212yes—
180#2511C2212yes—
181#2511C2212yes—
182#2509C2212yes—
183#2509C2211yescharacteristic
184#2509C2211yescharacteristic
185#2509C2212yes—
186#2508C2212yes—
187#2508C2212yes—
188#2508C2212yes—
189#2508C2212yes—
190#2508C2212yes—
191#2508C2212yes—
192#2508C2212yes—
193#2507C2212yes—
194#2507C2212yes—
195#2507C2212yes—
196#2507C2214yes—
197#2507C2214yes—
198#2507C2212yes—
199#2507C2212yes—
200#2507C2212yes—
201#2506C2212yes—
202#2506C2212yes—
203#2506C2212yes—
204#2506C2212yes—
205#2503C2212yes—
206#2497C2212yes—
207#2497C2212yes—
208#2496C2212yes—
209#2496C2212yes—
210#2496C2214yes—
211#2496C2212yes—
212#2495C2212yes—
213#2494C2212yes—
214#2489C2212yes—
215#2489C2212yes—
216#2469C2212yes—
217#2465C2214yes—
218#2462C2214yes—
219#2462C2214yes—
220#2462C2214yes—
221#2454C2212yes—
222#2453C2212yes—
223#2453C2212yes—
224#2453C2212yes—
225#2453C2212yes—
226#2453C2212yes—
227#2453C2212yes—
228#2453C2212yes—
229#2453C2211yescharacteristic
230#2453C2211yescharacteristic
231#2448C2212yes—
232#2448C2211yescharacteristic
233#2448C2212yes—
234#2447C2212yes—
235#2446C2212yes—
236#2446C2211yescharacteristic
237#2446C2212yes—
238#2442C2212yes—
239#2442C2212yes—
240#2441C2212yes—
241#2441C2212yes—
242#2440C2212yes—
243#2423C2212yes—
244#2402C2212yes—
245#2402C2212yes—
246#2401C2212yes—
247#2396C2212yes—
248#2378C2214yes—
249#2370C2212yes—
250#2370C2212yes—
251#2370C2212yes—
252#2367C2212yes—
253#2362C2212yes—
254#2356C2212yes—
255#2355C2211yescharacteristic
256#2355C2212yes—
257#2354C2211yescharacteristic
258#2351C2212yes—
259Q8×C4⋊C4C2211yescharacteristic
260Q8×C4⋊C4C2211yescharacteristic
261Q8×C4⋊C4C2211yescharacteristic
262Q8×C4⋊C4C2212yes—
263Q8×C4⋊C4C2212yes—
264D4×C4⋊C4C2211yescharacteristic
265#2346C2212yes—
266#2346C2212yes—
267#2345C2212yes—
268#2330C2212yes—
269#2330C2212yes—
270#2330C2214yes—
271#2330C2212yes—
272#2327C2212yes—
273#2320C2212yes—
274#2320C2212yes—
275#2319C2212yes—
276#2317C2212yes—
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2212yes—
279C4×C4⋊Q8C2211yescharacteristic
280C4×C4⋊Q8C2211yescharacteristic
281C4×C4⋊Q8C2211yescharacteristic
282C4×C4⋊Q8C2211yescharacteristic
283C4×#125C2211yescharacteristic
284C4×#125C2211yescharacteristic
285C4×#125C2212yes—
286C4×#126C2212yes—
287C4×#124C2211yescharacteristic
288C4×#124C2211yescharacteristic
289#2298C2212yes—
290#2295C2211yescharacteristic
291#2295C2211yescharacteristic
292#2295C2211yescharacteristic
293#2295C2212yes—
294#2295C2212yes—
295#2293C2211yescharacteristic
296C42×Q8C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C42×Q8C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2311yescharacteristic
302C2×C4⋊Q8C2312yes—
303C2×#126C2312yes—
304C2×#126C2314yes—
305C2×#126C2314yes—
306C2×#126C2314yes—
307C2×#125C2311yescharacteristic
308C2×#125C2311yescharacteristic
309C2×#125C2312yes—
310C2×#125C2312yes—
311C2×#125C2312yes—
312C2×#125C2312yes—
313C2×#125C2312yes—
314C2×#125C2314yes—
315C2×#125C2314yes—
316C2×#125C2314yes—
317C2×#125C2312yes—
318C2×#125C2314yes—
319C2×#124C2311yescharacteristic
320C2×#124C2311yescharacteristic
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2314yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2312yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C22×C4⋊C4C2312yes—
345#401C2312yes—
346#401C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2312yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2312yes—
379#400C2312yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2312yes—
385#400C2312yes—
386#400C2312yes—
387#400C2314yes—
388#399C2314yes—
389#399C2314yes—
390#399C2312yes—
391#399C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2312yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2312yes—
420#398C2312yes—
421#398C2312yes—
422#398C2312yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2312yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2312yes—
434#398C2312yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2312yes—
445#397C2312yes—
446#397C2312yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2312yes—
457#396C2312yes—
458#396C2314yes—
459#396C2312yes—
460#396C2314yes—
461#396C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#395C2312yes—
468#395C2314yes—
469#393C2314yes—
470#393C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2311yescharacteristic
475#391C2312yes—
476#391C2311yescharacteristic
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2311yescharacteristic
483#391C2312yes—
484#391C2311yescharacteristic
485#391C2312yes—
486#391C2312yes—
487#391C2311yescharacteristic
488#391C2311yescharacteristic
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2314yes—
493#391C2311yescharacteristic
494#391C2311yescharacteristic
495#391C2311yescharacteristic
496#391C2312yes—
497#391C2311yescharacteristic
498#390C2312yes—
499#390C2311yescharacteristic
500#390C2312yes—
501#390C2311yescharacteristic
502#390C2312yes—
503#390C2311yescharacteristic
504#390C2311yescharacteristic
505#389C2311yescharacteristic
506#389C2312yes—
507#389C2311yescharacteristic
508#389C2311yescharacteristic
509#389C2311yescharacteristic
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2311yescharacteristic
521#389C2312yes—
522#389C2312yes—
523#389C2311yescharacteristic
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2311yescharacteristic
536#389C2311yescharacteristic
537#389C2314yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#389C2311yescharacteristic
548#389C2312yes—
549#389C2312yes—
550#389C2311yescharacteristic
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2314yes—
555#389C2312yes—
556#389C2312yes—
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2312yes—
567#389C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2311yescharacteristic
574#389C2314yes—
575#389C2314yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2312yes—
584#389C2312yes—
585#389C2314yes—
586#389C2314yes—
587#389C2314yes—
588#389C2311yescharacteristic
589#389C2312yes—
590#389C2314yes—
591#389C2314yes—
592#389C2311yescharacteristic
593#389C2312yes—
594#389C2311yescharacteristic
595#388C2312yes—
596#388C2312yes—
597#388C2312yes—
598#388C2314yes—
599#388C2314yes—
600#388C2312yes—
601#388C2314yes—
602#388C2312yes—
603#388C2314yes—
604#388C2314yes—
605#388C2312yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2312yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2312yes—
620#388C2312yes—
621#388C2312yes—
622#387C2312yes—
623#387C2312yes—
624#387C2312yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2312yes—
629#387C2314yes—
630#387C2314yes—
631#387C2312yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2312yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2312yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2312yes—
661#387C2312yes—
662#387C2312yes—
663#387C2312yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2312yes—
672#387C2312yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2312yes—
686#387C2312yes—
687#387C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#384C2311yescharacteristic
695#384C2311yescharacteristic
696#384C2311yescharacteristic
697#384C2311yescharacteristic
698#384C2312yes—
699#384C2311yescharacteristic
700#384C2312yes—
701#384C2312yes—
702#384C2312yes—
703#384C2312yes—
704#384C2314yes—
705#384C2312yes—
706#384C2314yes—
707#384C2312yes—
708#384C2312yes—
709#384C2312yes—
710#384C2312yes—
711#384C2314yes—
712#383C2312yes—
713#383C2314yes—
714#383C2314yes—
715#383C2314yes—
716#382C2311yescharacteristic
717#382C2311yescharacteristic
718#382C2312yes—
719#382C2312yes—
720#382C2312yes—
721#382C2314yes—
722#382C2311yescharacteristic
723#382C2311yescharacteristic
724#382C2314yes—
725#382C2312yes—
726#382C2314yes—
727#382C2314yes—
728#382C2314yes—
729#382C2314yes—
730#382C2314yes—
731#382C2314yes—
732#382C2312yes—
733#382C2314yes—
734#381C2314yes—
735#381C2314yes—
736#380C2312yes—
737#380C2312yes—
738#380C2314yes—
739#380C2314yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2314yes—
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2314yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2314yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800#376C2312yes—
801#376C2312yes—
802#376C2312yes—
803#376C2314yes—
804#376C2314yes—
805C43C2312yes—
806C43C2311yescharacteristic
807C43C2311yescharacteristic
808C43C2311yescharacteristic
809C43C2312yes—
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2411yescharacteristic
813C22×Q8C2411yescharacteristic
814C22×Q8C2412yes—
815C22×Q8C2412yes—
816C22×D4C2411yescharacteristic
817C23×C4C2412yes—
818C23×C4C2414yes—
819C4⋊Q8—24no—
820C4⋊Q8—24no—
821C4⋊Q8—42no—
822C4⋊Q8—44no—
823#126—44no—
824#126—84no—
825#126—84no—
826#126—84no—
827#125—24no—
828#125—24no—
829#125—44no—
830#125—44no—
831#125—44no—
832#125—44no—
833#125—44no—
834#125—48no—
835#125—82no—
836#125—84no—
837#125—84no—
838#125—84no—
839#124—24no—
840#124—42no—
841C22⋊Q8—48no—
842C22⋊Q8—44no—
843C4×Q8—24no—
844C4×Q8—28no—
845C4×Q8—24no—
846C4×Q8—24no—
847C4×Q8—24no—
848C4×Q8—24no—
849C4×Q8—42no—
850C4×Q8—44no—
851C4×Q8—42no—
852C4×Q8—44no—
853C4×Q8—44no—
854C4×Q8—44no—
855C4×Q8—42no—
856C4×Q8—42no—
857C4×Q8—42no—
858C4×Q8—82no—
859C4×Q8—82no—
860C4×D4—24no—
861C4×D4—44no—
862#117—28no—
863#117—44no—
864C2×C4⋊C4—44no—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2411yescharacteristic
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2411yescharacteristic
910C2×C4⋊C4C2411yescharacteristic
911C2×C4⋊C4C2411yescharacteristic
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2411yescharacteristic
914C2×C4⋊C4C2411yescharacteristic
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C42C2411yescharacteristic
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2412yes—
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994C2×C42C2411yescharacteristic
995C2×C42C2411yescharacteristic
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2412yes—
1000C2×C42C2412yes—
1001C2×C42C2412yes—
1002C2×C42C2414yes—
1003C2×C42C2411yescharacteristic
1004C2×C42C2412yes—
1005C2×C42C2411yescharacteristic
1006C2×C42C2411yescharacteristic
1007C2×C42C2411yescharacteristic
1008C2×C42C2411yescharacteristic
1009C2×C42C2411yescharacteristic
1010C2×C42C2414yes—
1011C2×C42C2414yes—
1012C2×C42C2412yes—
1013C2×C42C2411yescharacteristic
1014C2×C42C2411yescharacteristic
1015C2×C42C2412yes—
1016C2×C42C2414yes—
1017C2×C42C2414yes—
1018C2×C42C2414yes—
1019C2×C42C2411yescharacteristic
1020C2×C42C2412yes—
1021C2×C42C2414yes—
1022C2×C42C2412yes—
1023C2×C42C2412yes—
1024C2×C42C2411yescharacteristic
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2414yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2411yescharacteristic
1056#95C2411yescharacteristic
1057#95C2412yes—
1058#95C2411yescharacteristic
1059#95C2411yescharacteristic
1060#95C2411yescharacteristic
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2411yescharacteristic
1065#95C2412yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2412yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2412yes—
1077#95C2414yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2414yes—
1082#95C2412yes—
1083#95C2414yes—
1084#95C2412yes—
1085#95C2414yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2412yes—
1089#95C2414yes—
1090#95C2414yes—
1091#95C2412yes—
1092#95C2414yes—
1093#95C2412yes—
1094#95C2412yes—
1095#95C2414yes—
1096#95C2412yes—
1097#95C2412yes—
1098#95C2412yes—
1099#95C2414yes—
1100#95C2412yes—
1101#95C2414yes—
1102#95C2412yes—
1103#95C2414yes—
1104#95C2412yes—
1105#95C2412yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119C24C2512yes—
1120C2×Q8—22no—
1121C2×Q8—22no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—24no—
1125C2×Q8—22no—
1126C2×Q8—22no—
1127C2×Q8—22no—
1128C2×Q8—22no—
1129C2×Q8—22no—
1130C2×Q8—24no—
1131C2×Q8—42no—
1132C2×Q8—41no—
1133C2×Q8—41no—
1134C2×Q8—42no—
1135C2×Q8—42no—
1136C2×Q8—42no—
1137C2×Q82−1+414yes—
1138C2×D4—22no—
1139C2×D4—22no—
1140C2×D4—22no—
1141C22×C4—24no—
1142C22×C4—24no—
1143C22×C4—24no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2512yes—
1154C22×C4C2514yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2511yescharacteristic
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2514yes—
1161C22×C4C2511yescharacteristic
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2514yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2511yescharacteristic
1172C22×C4C2511yescharacteristic
1173C22×C4C2514yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2511yescharacteristic
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C22×C4C2511yescharacteristic
1181C4⋊C4—24no—
1182C4⋊C4—22no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—28no—
1186C4⋊C4—22no—
1187C4⋊C4—22no—
1188C4⋊C4—24no—
1189C4⋊C4—22no—
1190C4⋊C4—22no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—22no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—28no—
1208C4⋊C4—22no—
1209C4⋊C4—24no—
1210C4⋊C4—22no—
1211C4⋊C4—22no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—22no—
1215C4⋊C4—44no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—42no—
1222C4⋊C4—44no—
1223C4⋊C4—42no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—42no—
1230C4⋊C4—41no—
1231C4⋊C4—41no—
1232C4⋊C4—41no—
1233C4⋊C4—42no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—42no—
1256C4⋊C4—42no—
1257C4⋊C4—42no—
1258C4⋊C4—44no—
1259C4⋊C4—44no—
1260C4⋊C4—42no—
1261C4⋊C4—44no—
1262C4⋊C4—42no—
1263C4⋊C4—44no—
1264C4⋊C4—44no—
1265C4⋊C4—44no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—44no—
1270C4⋊C4—42no—
1271C4⋊C4—42no—
1272C4⋊C4—42no—
1273C4⋊C4—42no—
1274C4⋊C4—42no—
1275C4⋊C4—42no—
1276C4⋊C4—42no—
1277C4⋊C4—42no—
1278C4⋊C42−1+414yes—
1279C22⋊C4—28no—
1280C22⋊C4—24no—
1281C22⋊C4—24no—
1282C22⋊C4—24no—
1283C22⋊C4—24no—
1284C22⋊C4—42no—
1285C22⋊C4—42no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—42no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—42no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C42—28no—
1300C42—28no—
1301C42—24no—
1302C42—24no—
1303C42—24no—
1304C42—22no—
1305C42—22no—
1306C42—24no—
1307C42—24no—
1308C42—24no—
1309C42—22no—
1310C42—22no—
1311C42—22no—
1312C42—22no—
1313C42—22no—
1314C42—24no—
1315C42—24no—
1316C42—22no—
1317C42—22no—
1318C42—24no—
1319C42—22no—
1320C42—22no—
1321C42—22no—
1322C42—22no—
1323C42—24no—
1324C42—41no—
1325C42—41no—
1326C42—42no—
1327C42—42no—
1328C42—44no—
1329C42—44no—
1330C42—44no—
1331C42—41no—
1332C42—41no—
1333C42—44no—
1334C42—44no—
1335C42—41no—
1336C42—42no—
1337C42—44no—
1338C42—42no—
1339C42—42no—
1340C422−1+414yes—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23C2611yescharacteristic
1349Q8—28no—
1350Q8—44no—
1351Q8—48no—
1352Q8—44no—
1353Q8—44no—
1354Q8—84no—
1355D4—44no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—21no—
1362C2×C4—22no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—24no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—21no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—22no—
1410C2×C4—21no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—21no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—22no—
1421C2×C4—24no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—24no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—22no—
1437C2×C4—24no—
1438C2×C4—24no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—22no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—22no—
1448C2×C4—48no—
1449C2×C4—164no—
1450C2×C4C2×2−1+414yes—
1451C2×C4C2×2−1+414yes—
1452C2×C4C2×2−1+412yes—
1453C2×C4C2×2−1+412yes—
1454C2×C4C2×2−1+412yes—
1455C2×C4C2×2−1+412yes—
1456C2×C4C2×2−1+412yes—
1457C2×C4#58512yes—
1458C2×C4#58512yes—
1459C2×C4#58512yes—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—42no—
1465C22—42no—
1466C22—42no—
1467C22C22×2−1+411yescharacteristic
1468C22C22×2−1+411yescharacteristic
1469C22C22×2−1+411yescharacteristic
1470C22C2×#58511yescharacteristic
1471C22C2×#58511yescharacteristic
1472C22C2×#58511yescharacteristic
1473C22H(7,𝔽2)11yescharacteristic
1474C4—24no—
1475C4—24no—
1476C4—22no—
1477C4—22no—
1478C4—42no—
1479C4—42no—
1480C4—42no—
1481C4—41no—
1482C4—41no—
1483C4—41no—
1484C4—42no—
1485C4—44no—
1486C4—42no—
1487C4—41no—
1488C4—41no—
1489C4—42no—
1490C4—42no—
1491C4—42no—
1492C4—42no—
1493C4—44no—
1494C4—41no—
1495C4—41no—
1496C4—44no—
1497C4—41no—
1498C4—41no—
1499C4—42no—
1500C4—41no—
1501C4—41no—
1502C4—42no—
1503C4—44no—
1504C4—42no—
1505C4—42no—
1506C4#355514yes—
1507C4#356314yes—
1508C2—82no—
1509C2C2×#356311yescharacteristic
1510C2C2×#355511yescharacteristic
1511C2#6282711yescharacteristic
1512C2#6292611yescharacteristic
1513C2#6295211yescharacteristic
1514C2#6295211yescharacteristic
1515C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59445C2semidirect
4. #57690C2semidirect
5. #56536C2semidirect
6. #55385C2semidirect
7. #53107C2semidirect
8. #53036C2semidirect
9. #50056C2semidirect
11. #46069C2semidirect
13. #45219C2semidirect
14. #42972C2semidirect
16. #42774C2semidirect
17. #42728C2semidirect
18. #40075C2semidirect
19. #39754C2semidirect
20. #39635C2semidirect
21. #39180C2semidirect
22. #39081C2semidirect
25. #38227C2semidirect
28. #37328C2semidirect
29. #36574C2semidirect
30. Q8×#125C2semidirect
32. #35208C2semidirect
33. #35208C2semidirect
34. #34951C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#594452
#594352
#594292
#576902
#565362
#553852
#531072
#530362
#500562
#463472
#460692
#454032
#452192
#429722
#428452
#427742
#427282
#400752
#397542
#396352
#391802
#390812
#389772
#389662
#382272
#376372
#373532
#373282
#365742
Q8×#1252
#363122
#352082
#349512
#349022